“The Mountaintop’’ premiered in London in 2009, when the playwright was in her 20s, and it won the 2010 Olivier Award for best new play, edging out “Red,” “Jerusalem,” and “Enron.” It has since been on Broadway.

Despite these credentials, Underground Railway Theater’s 90-minute, one-act production at Central Square Theater, directed by Megan Sandberg-Zakian, offers a case study in that all-too-familiar theater phenomenon: When Bad Plays Happen to Good Actors. Here, the performers are Maurice Emmanuel Parent, as King, and Kami Rushell Smith as Camae, a maid with an outsize personality who shows up in King’s motel room and seems bent on challenging him at every turn.

As they engage in a protracted conversation that is freewheeling, contentious, intermittently flirtatious, and ultimately fraught with revelation, Parent and especially Smith bring their considerable talent and passion to bear. Yet it can only come to naught when the playwright herself seems to lack confidence in the material, erratically veering from drama to broad humor to a kind of magic realism.

The weaknesses of “The Mountaintop’’ are especially glaring when the play is compared to Tracey Scott Wilson’s “The Good Negro,’’ which premiered at New York’s Public Theater in 2009 and got a Boston staging by Company One a year later. Exploring the internal and external struggles of a King-like civil rights leader who finds himself at a historical crossroads, “The Good Negro’’ dug deep. “The Mountaintop’’ does not.

The title of Hall’s play is drawn from King’s famed “I’ve Been to the Mountaintop’’ speech. As “The Mountaintop’’ begins, a weary King arrives in Room 306 of the Lorraine Motel in Memphis, having just given that speech. A red neon chevron is blinking on and off next to the motel sign. His room, designed by Susan Zeeman Rogers, is a drab affair: two beds, a bureau, a lamp. It’s April 3, 1968, the night before King was slain.

Hall is at pains to show us that in some respects, King was a man like any other. After he enters the bathroom, rehearsing aloud a line from an upcoming sermon, we hear the toilet flush. He constantly needs a smoke — an ashtray is filled with cigarette butts — and there are holes in his socks. It is made clear that King has smelly feet. Insecure about looking old, he asks Camae whether he should shave his mustache. On edge because of the death threats he has received, he responds with alarm to the periodic thunderclaps outside, at one point even rushing across the room.

Camae is certainly not intimidated by him, openly questioning the efficacy of King’s peaceful protest marches in overcoming racial injustice. “Walking will only get you so far, Preacher King,’’ she declares. When he tartly responds, “We’re not just walking; we’re marching,’’ Camae’s retort is swift: “Whatever it is, it ain’t working.’’ She dons King’s jacket and shoes, clambers up on a bed, and proceeds to deliver a fiery speech loaded with the kind of defiantly confrontational rhetoric she thinks he should employ.

Smith skillfully executes the scene, one of several that underscore the extent to which King plays second fiddle in “The Mountaintop.’’ Yes, it’s engrossing to watch Parent’s King agonize over all the work he still has to do and to hear him voice an unflagging commitment to the cause of the downtrodden. But Parent is in a no-win situation. On the one hand, King is such a familiar icon, his face and voice so readily available to us in archival footage, that to play him convincingly is an enormous challenge. On the other hand, Hall’s version of King lacks the stature to make us believe we are truly watching one of history’s giants onstage.

“The Mountaintop’’ really starts to fall apart, though, when the playwright resorts to a twist whose nature I won’t disclose except to say that it’s central to the play — and that it greatly intensifies the tonal dissonance that makes “The Mountaintop,’’ despite the occasional creative peaks, such an unsatisfying climb.

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